{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T00:29:47Z","timestamp":1675211387661},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6493,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,6]]},"abstract":"<jats:p>In Part I, we produced a Gentzenization L<jats:sub>6<\/jats:sub>LBQ of the distributionless relevant logic LBQ, which contained just the one structural connective \u2018:\u2019 and no structural rules. We compared it with the corresponding \u201cright-handed\u201d system and then proved interpolability and decidability of LBQ. Knowledge of Part I is presupposed.<\/jats:p><jats:p>In Part II of this paper, we will establish Gentzenizations, with appropriate interpolation and decidability results, for the further distributionless logics LDWQ, LTWQ<jats:sup>o<\/jats:sup>, LEWQ<jats:sup>ot<\/jats:sup>, LRWQ, LRWKQ and LRQ, using essentially the same methods as were used for LBQ in Part I. LRWQ has been Gentzenized by Grishin [2], but the interpolation result is new and the decidability result is proved by a substantial simplification of his method. LR has been Gentzenized and shown to be decidable by Meyer in [5], by extending a method of Kripke in [3], and McRobbie has proved interpolation for it in [4], but here the Gentzenization and interpolation results are extended to quantifiers.<\/jats:p><jats:p>We axiomatize these logics as follows. The primitives and formation rules are as before, except that LTWQ and LEWQ require the extra primitive \u2018o\u2019, a 2-place connective (called \u2018fusion\u2019), and LEWQ also requires \u2018t\u2019, a sentential constant.<\/jats:p>","DOI":"10.2307\/2275667","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:58:29Z","timestamp":1146956309000},"page":"379-401","source":"Crossref","is-referenced-by-count":6,"title":["Gentzenizations of relevant logics without distribution. II"],"prefix":"10.1017","volume":"61","author":[{"given":"Ross T.","family":"Brady","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200017345_ref003","first-page":"324","volume":"24","author":"Kripke","year":"1959","journal-title":"The problem of entailment"},{"key":"S0022481200017345_ref004","unstructured":"McRobbie M. A. , A proof-theoretic investigation of relevant and modal logics, Ph.D. Thesis , Australian National University, Canberra, 1979."},{"key":"S0022481200017345_ref002","first-page":"316","volume-title":"Studies in nonclassical logics and set theory","author":"Grishin","year":"1979"},{"key":"S0022481200017345_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF00935747"},{"key":"S0022481200017345_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF00249365"},{"key":"S0022481200017345_ref005","unstructured":"Meyer R. K. , Topics in modal and many-valued logic, Ph.D. Thesis , University of Pittsburgh, Pittsburgh, Pennsylvania, 1966."},{"key":"S0022481200017345_ref006","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093887722"},{"key":"S0022481200017345_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF01349560"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017345","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T21:28:55Z","timestamp":1557696535000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017345\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,6]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1996,6]]}},"alternative-id":["S0022481200017345"],"URL":"https:\/\/doi.org\/10.2307\/2275667","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,6]]}}}